{"id":"W2314635900","doi":"10.4153/cjm-2011-036-9","title":"The Cubic Dirac Operator for Infinite-Dimensonal Lie Algebras","year":2011,"lang":"en","type":"article","venue":"Canadian Journal of Mathematics","topic":"Algebraic structures and combinatorial models","field":"Mathematics","cited_by":2,"is_retracted":false,"has_abstract":true,"ca_institutions":"University of Toronto","funders":"","keywords":"Mathematics; Pure mathematics; Bilinear form; Lie algebra; Affine Lie algebra; Lie conformal algebra; Non-associative algebra; Clifford algebra; Dirac operator; Killing form; Casimir element; Rank (graph theory); Algebra over a field; Adjoint representation of a Lie algebra; Combinatorics; Current algebra","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.0004441691,0.0001745285,0.00030412,0.0008350823,0.001077773,0.0009959808,0.0004909039,0.0004250045,0.002912411],"category_scores_gemma":[0.0009279696,0.0001531573,0.0002572298,0.0004736229,0.001627095,0.00121995,0.001024954,0.0007992198,0.000236966],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001176726,"about_ca_system_score_gemma":0.001033131,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.002629666,"about_ca_topic_score_gemma":0.002704221,"domain_scores_codex":[0.9997475,0.00003638159,0.00001228111,0.00002250018,0.0001300496,0.00005140185],"domain_scores_gemma":[0.9995754,0.00006454364,0.00006305739,0.00004576415,0.000118041,0.0001330975],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00002415506,0.00001632746,0.0003116086,0.00001906334,0.000002452047,0.0001719021,0.0001736328,0.001070957,0.002639978,0.9925258,0.0004092236,0.002634859],"study_design_scores_gemma":[0.00002427654,0.0000270122,0.0005646131,0.00001214744,0.000003433279,0.0002671924,0.0002091543,0.02473591,0.001884599,0.9701214,0.002128969,0.00002115623],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.9162676,0.0002552923,0.04298124,0.0007585305,0.0001038291,0.00003381952,0.00009611324,0.0001172218,0.03938618],"genre_scores_gemma":[0.9902954,0.00007819706,0.004550003,0.00008044243,0.00003779491,0.00001357207,0.00004460546,0.00001145326,0.004888563],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.002912411,"threshold_uncertainty_score":0.009742975,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.07430041863544565,"score_gpt":0.2724199684682532,"score_spread":0.1981195498328076,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}